Question

计算：1/1*2+1/2*3+1/3*4+…+1/2004*2005=（ ）

如有简便方法，请把过程写出来！谢谢~~~

Answer 1

你好！！！

1/1*2
=1/1-1/2

1/2*3
=1/2-1/3

这样类推。

1/1*2+1/2*3+1/3*4+…+1/2004*2005
=1/1-1/2005
=2004/2005

还有什么不明白的地方再问我。

谢谢！！！

Answer 2

1/n*(n+1)=1/n-1/(n+1);
(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/2003-1/2004)+(1/2004-1/2005)
=1-1/2005=2004/2005;

Answer 3

1/1*2+1/2*3+1/3*4+…+1/2004*2005
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2004-1/2005)
=1-1/2+1/2-1/3……+1/2004-1/2005
=1-1/2005
=2004/2005

Answer 4

1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
......
1/(2004*2005)=1/2004-1/2005
原式=1-1/2+1/2-1/3+......+1/2004-1/2005
=1-1/2005
=2004/2005